# MATH141: Mathematics 1C Part 1

This web page was constructed for the old version of MATH141 that I co-taught from 2003-2008. I don't make any promises as to whether anything on here is relevant for the new version of MATH141 that I am co-teaching in 2015.

http://www.its.uow.edu.au.

## Contents

This page mostly contains material for the subjects I teach: fundamentals, differentiation, polar co-ordinates, integration. Some resources for matrices are also discussed.

## Student Consultation

Mark's consolation hours are:
 Monday 15.30-17.30 Wednesday 10.30-12.30
His room is 15.G26. If you cannot come at these times, contact Mark to arrange an appointment at a mutually convenient time.

## Content of MATH141

MATH141 is divided into six sections. The names of these sections and the content covered in each section are approximately as follows:

1. Fundamentals. There are seven (*) hours of lectures on this topic. The contents of this section are listed here.
2. Differentiation. There are eight (*) hours of lectures on this topic. The contents of this section are listed here.
3. Polar Coordinates. There are three (*) hours of lectures on this topic. The contents of this section are listed here.
4. Integration. There are four hours of lectures on this topic. The contents of this section are listed here.
5. Matrices and Determinants. There are thirteen (*) hours of lectures on this topic.
1. Index and Sigma Notation (Sections 5.2 to 5.4).
2. Introduction to Matrices (Sections 5.5 to 5.10).
3. Application of Matrices to Systems of Equations (Sections 5.11 to 5.17).
4. Determinants (Sections 5.18 to 5.20).
5. Eigenvalues and eigenvectors (Section 5.21).
6. Vector Geometry. There are twelve (*) hours of lectures on this topic.
1. Coordinates in Space (Section 6.1).
2. Introduction to Vectors (Section 6.2).
3. Vector Arithmetic (Section 6.3).
4. Unit Vectors (Section 6.4).
5. Projections (Section 6.5).
6. Dot product of Two Vectors (Section 6.6).
7. The Straight Line (Section 6.7).
8. Cross Product of Two Vectors (Section 6.8).
9. Planes (Section 6.9).
(*) The number of lectures may be lower than stated due to public holidays.

The Summertime Maths Web Page has some great resources for this subject. To find them look at the right-hand side of the page and click on `DVD Topics/Contents'. There are many additional features of interest on this site. You are encouraged to investigate!

The math centre page in the UK has some good resources.

## Basic Skills Test

### Sample questions from the Basic Skills Test

This file contains nine questions from previous basic skill tests. I've chosen questions that over 50% of students answered incorrectly.

If your best mark is 16+ then you receive a bonus of 3% at the end of this course. Congratulations!

If your best mark is 15 then you receive a bonus of 1% at the end of this course. Congratulations.

If your best mark is less than 15 I am interested in how much you have improved. If you have improved by approximately 5 or better, well done! If you have improved by less than 5 you need to work harder. If your score has decreased you need to get off your backside and do some work.

PDF file containing your first BST mark, your second BST mark and your best BST mark. The results are sorted numerically according to student number. These file only contains the marks for those students who took the second BST at the scheduled time. If you had special consideration and took the BST afterwards your mark is not recorded here. However, you should know what your mark is because I marked your BST paper as soon as you finished the test!

Note. No-one scored `0'. A mark of `0' means that you failed to attend the test. A score of 0.0 means that you attended the test and didn't fill in any answers on the answer sheet. Seven students took the test paper and didn't put either their name or their student number on the test. These students scored 0.

## Mid-Session Test

Students always ask me what is on the mid-session test. I am always surprised by this question because I've assumed that students know that questions are what on a test paper...

The mid-session test paper usually contains 14 questions from the fundamentals/differentiation component of the course and 11 questions from the matrices part of the course. The questions from the fundamentals/differentiation part of the course split often approximately 50-50 between fundamentals and differentiation. If there are seven differentiation questions then these will usually comprise five questions on `elementary differentiation' and two questions from the preceding topics (`functions' and `limits').

In the above paragraph the words `usually', `often', `approximately' indicate that these are guidelines to what material might appear on the mid-session paper. There is no guarantee that the questions will be divided in this way.

A sample test paper. Attempt this test paper under exam conditions.

PDF file containing your fist BST mark, your second BST mark, your best BST mark and your mid-session test mark, sorted numerically according to student number. Note: You do not need to pass the mid-session test to pass the course. Obviously it is desirable to do well on the test...

2015 PDF file containing marks from the MST, sorted numerically according to student number. This file only contains the marks for those students who took the MST at the scheduled time. If you had special consideration and took the MST afterwards your mark is not recorded here.

If you attended the test but your mark does not appear please contact me ASAP. Due the the scanning process used to mark the papers there are a few marks that I can not enter because I do not know who the student is!

## Fundamentals

Each over-head will print out as one sheet of A4.

### Fundamentals: Worksheets

Each worksheet will print out on one side of A4 paper.

 Lecture 2 Indices Solutions Surds solutions Lecture 3 Logarithms solutions Factorisation solutions Algebraic Fractions solutions Lecture 4 Functions solutions Quadratic Equations solutions Lecture 5 Geometry solutions Trigonometry solutions

## Differentiation

### Lecture Notes

Lecture notes are available in two forms. The single form has one overhead per side of A4. The double form has two overheads per side of A4. Thus you need to print fewer sides of A4 if you select the double option. However, the quality of the PDF file is lower for the double form.

1. Functions: single double
2. Limits: single double
3. Elementary differentiation: single double
4. Hyperbolic functions: single double
5. One-to-one and inverse functions: single double
6. Inverse Trigonometric Functions single double
7. Inverse Hyperbolic Functions single double
8. The Derivative of an Inverse Function single double
9. Logarithmic Differentiation single double
10. Implicit Differentiation single double
11. Parametric Equations and Curves: single double

### Why are we interested in...?

The aim of this section is to give a hint as to why a certain topic is more interesting than you might think! It shows some of the applications of the material that we cover in lecture to real problems.

### Multiple Choice questions on Differentiation topics

Here are some multiple-choice questions on various parts of the differentiation notes.

### Differentiation Worksheets

 Limits solutions elementary differentiation solutions. implicit differentiation solutions. parametric differentiation solutions.

## Polar coordinates and polar curves

If you run out of polar graph paper you can make your own at http://incompetech.com/graphpaper/. (Scroll down to the Speciality section).

### Lecture Notes

Lecture notes are available in two forms. The single form has one overhead per side of A4. The double form has two overheads per side of A4. Thus you need to print fewer sides of A4 if you select the double option. However, the quality of the PDF file is lower for the double form.

 1 Polar coordinates single double 2 Polar curves single double

### Why are we interested in...?

The aim of this section is to give a hint as to why a certain topic is more interesting than you might think! It shows some of the applications of the material that we cover in lecture to real problems.

## Integration

### Integration notes

Lecture notes are available in two forms. The single form has one overhead per side of A4. The double form has two overheads per side of A4. Thus you need to print fewer sides of A4 if you select the double option. However, the quality of the PDF file is lower for the double form.

 3.1 The indefinite integral and the definite integral single double 3.1.1 The indefinite integral 3.2 The definite integral 3.2.3 Properties of integrals 3.2.4 Revision questions 2. Methods of Integration: 3.3.1-3.3.3 single double 3.3.1 Integrals by inspection 3.3.2 Simplifying Integrals 3.3.3 Using Integral Tables 3. Methods of Integration: 3.3.5-3.3.7 single double 3.3.5 Algebraic Substitution 3.3.6 Integration of the form... 3.3.7 Revision Questions

### Integration worksheets

 Integration worksheet solutions Integration Exam Questions: 2000-2002 (1)

(1) The answers are included with the questions. There is a page of questions and then a page of answers.

## Tutorials (Wollongong campus)

 Week 2 solutions Week 3 solutions Week 4 solutions Week 5 solutions Week 6 solutions Week 7 solutions Week 8 solutions Week 9 solutions Week 10 solutions Week 11 solutions Week 12 solutions Week 13 solutions

## Previous exam papers and worked solutions

The course handbook contains exam papers from 2001-2003 with selected answers.

 Exam Solutions 2000 * Question 1 Question 2 Question 3 Question 4 2001 ^ Question 1 Question 2 Question 3 Question 4 2002 ^ Question 1 Question 2 Question 3 Question 4 2003 ^ Question 1 Question 2 Question 3 Question 4 2004 * Question 1 Question 2 Question 3 Question 4 2005 * Question 11 Question 2 Question 3 Question 4 2006 * Question 1 Question 2 Question 3 Question 4 2007 * Questions 1-4 2 * does not include tables of integrals ^ includes tables of integrals

1. 2005. Answer to question 1(a)(iv). The answer to the question is wrong. The right answer is 5.

(The given answer is correct if in the question the value of a was a1j).

2. 2007. Page five of the answers to question (4) is missing

## Matrices

A link to an on-line resource for matrix calculations. You will need to explore the pages a little.

## Vectors

Teaching notes for vectors (from 2006) are available on this web page. These notes may use a different notation to the ones that your lecturer is using and may contain material that is not begin taught this year. However, you may find them useful.

## Timetable for study assistance during study week

At Wollongong the revision classes are:

• Monday 2nd June. 13.30-15.30 in 15.107.
• Wednesday 4th June . Problem solving class. 09.30-12.30 in 67.107. This class will go through the 2003 MATH187 exam paper. The questions on matrices and vectors on this exam paper were the same as on the 2003 MATH141 exam paper and will be done first.
• Wednesday 4th June . 15.30-17.30 in 15.107.
• Thursday 7th June. 12.30-14.30 in 15.107
• Friday 8th June. 11.30-13.30 in 15.107.

At Loftus the revision classes are:

• Tuesday 3rd June 2008. 16.30-18.30 in LF.G03.
• Thursday 7th June 2008. 15.45-17.45 in LF.G06.

Notes:

1. Staff will not be available for assistance outside these times.
2. There will be a roster system for answering questions and a limit of 3 questions per student at any one time.
3. Students should bring with them their lecture notes and/or attempted exercises when asking for assistance.
4. Solution to past papers (2000-2007) are available via this web-page.
5. Loftus students are welcome to attend the sessions at Wollongong.